paper.tex

国外免费地震资料处理软件包

\title{Field recording geometry}
\author{Jon Claerbout} 
\label{paper:fld}

\maketitle

\pagenumbering{arabic}  % hopefully, this causes page 1 to be on chapter 1 page.

%{\em \today .  This chapter is owned by JFC.}

\par
The basic equipment for reflection seismic prospecting
is a source for impulsive sound waves,
a geophone (something like a microphone),
and a multichannel waveform display system.
A survey line is defined along the earth's surface.
It could be the path for a ship,
in which case the receiver is called a hydrophone.
About every 25 meters the source is activated, and
the echoes are recorded nearby.
The sound source and receiver have almost no directional tuning capability
because the frequencies that penetrate the earth
have wavelengths longer than the ship.
Consequently, echoes can arrive from several directions at the same time.
It is the joint task of geophysicists and geologists
to interpret the results.
Geophysicists assume the quantitative, physical, and statistical tasks.
Their main goals, and the goal to which this
book is mainly directed, is to make good 
pictures of the earth's interior from the echoes.

\section{RECORDING GEOMETRY}

\par
Along the horizontal $x$-axis we define two points,
$s$, where the source (or shot or sender) is located,
and  $g$, where the geophone (or hydrophone or microphone) is located.
Then, define the \bx{midpoint}  $y$  between the
shot and geophone, and
define  $h$  to be half the horizontal \bx{offset}
between the shot and geophone:
%.ne 1.2i
\begin{eqnarray}
y\ \ &=&\ \ {g \ +\  s  \over 2 }
\label{eqn:0.1a}
\\
h\ \ &=&\ \ {g \ -\  s  \over 2 }
\label{eqn:0.1b}
\end{eqnarray}
The reason for using
{\em half}
the offset in the equations
is to simplify and symmetrize many later equations.
Offset is defined
with  $g - s$  rather than with  $s - g$  so that
positive offset means waves
moving in the positive  $x$ direction.
In the marine case, this means the ship is presumed to sail
negatively along the  $x$-axis.
In reality the ship may go either way,
and shot points may either increase or decrease as the survey proceeds.
In some situations you can clarify matters by setting the
field observer's shot-point numbers to negative values.
\par
Data is defined experimentally in the space of  $(s,\,g)$.
Equations~(\ref{eqn:0.1a}) and (\ref{eqn:0.1b})
represent a change of coordinates to the space of $(y,\,h)$.
Midpoint-offset coordinates are especially useful
for interpretation and data processing.
Since the data is also a function of the travel time  $t$,
the full dataset lies in a volume.
Because it is so difficult to make a satisfactory display of such a volume,
what is customarily done is to display slices.
The names of slices vary slightly from one company to the next.
The following names seem to be well known and clearly understood:
\begin{center}
\begin{tabular}{lp{2.75in}}
$(y,\ h = 0,\ t)$       & zero-offset section \\
$(y,\ h = h_{\rm min\,,}\  t)$ & near-trace section \\
$(y,\ h = \hbox{const} ,\  t)$ &        constant-offset section \\
$(y,\ h = h_{\rm max\,,}\  t)$ & far-trace section \\
$(y = \hbox{const} ,\  h,\  t)$ & common-midpoint gather \\
$(s = \hbox{const} ,\  g,\  t)$ & field profile (or common-shot gather) \\
$(s,\ g = \hbox{const} ,\  t)$ & common-geophone gather \\
$(s,\ g,\ t = \hbox{const} )$ & time slice \\
$(h,\ y,\ t = \hbox{const} )$ & time slice \\
%\end{tabbing}
\end{tabular}
\end{center}
\sx{time slice}
\sx{zero-offset section}
\sx{near-trace section}
\sx{section!near-trace}
\sx{section!zero-offset}
\par
\inputdir{XFig}
A diagram of slice names is in Figure~\ref{fig:sg}.
Figure~\ref{fig:cube} shows three slices from the data volume.
The first mode of display is ``engineering drawing mode.''
The second mode of display is on the faces of a cube.
But notice that although the data is displayed on the surface
of a cube, the slices themselves are taken from the interior of the cube.
The intersections of slices across one another are shown by dark lines.
\plot{sg}{width=6.0in}{
        Top shows field recording of marine seismograms from
        a shot at location  $s$  to geophones at locations labeled  $g$.
        There is a horizontal reflecting layer to aid interpretation.
        The lower diagram is called a \bx{stacking diagram}.
        (It is
        {\em not}
        a perspective drawing).
        Each dot in this plane depicts a possible seismogram.
        Think of time running out from the plane.
        The center geophone above (circled)
        records the seismogram (circled dot) that
        may be found in various geophysical displays.
        Lines in this $(s,g)$-plane are planes in the $(t,s,g)$-volume.
	Planes of various orientations have the names given in the text.
        }
%\activeplot{rick}{height=4.5in}{}{
%       Slices from a cube of data from the Grand Banks.
%       Left is ``engineering drawing'' mode.
%       At the right slices from within the cube are shown as faces on the cube.
%       (Data from Amoco.
%       Display via Rick Ottolini's movie program).
%       }
\inputdir{cube}
\plot{cube}{width=6.00in,height=8.0in}{
        Slices from within a cube of data.
        Top: Slices displayed as a mechanical drawing.
        Bottom: Same slices shown on perspective of cube faces.
%       (Push button to interact with Steve Cole's Cubeplot program.)
        }

\par
A common-depth-point (CDP) gather is defined
by the industry and by common usage
to be the same thing as a common-midpoint (CMP) gather.
But in this book
a distinction will be made.
A \bx{CDP gather} is a \bx{CMP gather} with its time
axis stretched according to some velocity model, say,
$$
(y=\hbox{const},\ h,\ \sqrt{t^2 - 4h^2 /v^2 }) \quad \quad
\hbox{common-depth-point gather}
$$
This offset-dependent stretching makes the time axis of the gather 
become more like a
{\em depth}
axis, thus providing the
{\em D} 
in CDP.
The stretching is called 
{\em 
\bx{normal moveout} correction
}
(NMO).
Notice that as the velocity goes to infinity, the amount of stretching
goes to zero.

\par
There are basically two ways to get two-dimensional information
from three-dimensional information.
The most obvious is to cut out the slices defined above.
A second possibility is to remove a dimension by summing over it.
In practice, the offset axis is the best candidate for summation.
Each CDP gather is summed over offset.
The resulting sum is a single trace.
Such a trace can be constructed at each midpoint.
The collection of such traces, a function of midpoint and time,
is called a CDP stack.
Roughly speaking, a CDP stack is like a zero-offset section,
but it has a less noisy appearance.
\par
The construction of a CDP stack requires that a numerical choice
be made for the moveout-correction velocity.
This choice is called the {\em stacking velocity.}
The stacking velocity may be simply someone's guess of the earth's velocity.
Or the guess may be improved by stacking with some trial velocities
to see which gives the strongest and least noisy CDP stack.
\par
Figures~\ref{fig:yc02} and~\ref{fig:yc20} show
typical marine and land \bx{profile}s
(common-shot gathers).

\inputdir{yc}
\sideplot{yc02}{height=4.0in,width=3.5in}{
        A seismic land profile.
        There is a gap where there are no receivers near the shot.
        You can see events of three different velocities.
%        Press button to change plot parameters.
        (Western Geophysical).
        }

\sideplot{yc20}{height=4.0in,width=3.5in}{
        A marine profile off the Aleutian Islands.
%        Press button to change plot parameters.
        (Western Geophysical).
        }

The land data has geophones on both sides of the source.
The arrangement shown is called an
{\em uneven \bx{split spread}.}
The energy source was a vibrator.
The marine data happens to nicely illustrate
two or three head waves.
\todo{define head waves?}
The marine energy source was an air gun.
These field profiles were each recorded with about 120 geophones.

\subsection{Fast ship versus slow ship}
\inputdir{sg}
For marine seismic data,
the spacing between shots $\Delta s$ is a function of the speed
of the ship and the time interval between shots.
Naturally we like $\Delta s$ small
(which means more shots)
but that means either the boat slows down,